Gillard bought the house in the working-class suburb of Altona some years ago, and lives there with partner Tim Mathieson, the report said.
The 48-year-old continued to stay there during and after the election when she was in Melbourne.
"There are security and other issues. I'm staying in my home in Altona and I very much enjoy that, but I suspect that there are some friends who deal with prime ministerial security who would wish for a different result," she said.
Gillard said she would work through the issue of where to live in the city, the AAP quoted her as saying. She is expected move into the Lodge when she is in Canberra, and Mathieson will go with her.
There were some small-scale repairs taking place and she would stay at the prime ministerial Kirribilli House when in Sydney, the Aussie premier said.